# clogf, clog, clogl

< c‎ | numeric‎ | complex

C
 Language Headers Type support Program utilities Variadic function support Error handling Dynamic memory management Date and time utilities Strings library Algorithms Numerics Input/output support Localization support Atomic operations (C11) Thread support (C11) Technical Specifications

Complex number arithmetic
Types and the imaginary constant
 complex(C99) _Complex_I(C99) CMPLX(C11)
 imaginary(C99) _Imaginary_I(C99) I(C99)
Manipulation
 cimag(C99) creal(C99) carg(C99)
 cabs(C99) conj(C99) cproj(C99)
Power and exponential functions
 cexp(C99) clog(C99)
 cpow(C99) csqrt(C99)
Trigonometric functions
 ccos(C99) csin(C99) ctan(C99)
 cacos(C99) casin(C99) catan(C99)
Hyperbolic functions
 ccosh(C99) csinh(C99) ctanh(C99)
 cacosh(C99) casinh(C99) catanh(C99)

 Defined in header  float complex       clogf( float complex z ); (1) (since C99) double complex      clog( double complex z ); (2) (since C99) long double complex clogl( long double complex z ); (3) (since C99) Defined in header  #define log( z ) (4) (since C99)
1-3) Computes the complex natural (base-e) logarithm of z with branch cut along the negative real axis.
4) Type-generic macro: If z has type long double complex, clogl is called. if z has type double complex, clog is called, if z has type float complex, clogf is called. If z is real or integer, then the macro invokes the corresponding real function (logf, log, logl). If z is imaginary, the corresponding complex number version is called.

## Contents

### Parameters

 z - complex argument

### Return value

If no errors occur, the complex natural logarithm of z is returned, in the range of a strip in the interval [−iπ, +iπ] along the imaginary axis and mathematically unbounded along the real axis.

### Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• The function is continuous onto the branch cut taking into account the sign of imaginary part
• clog(conj(z)) == conj(clog(z))
• If z is -0+0i, the result is -∞+πi and FE_DIVBYZERO is raised
• If z is +0+0i, the result is -∞+0i and FE_DIVBYZERO is raised
• If z is x+∞i (for any finite x), the result is +∞+πi/2
• If z is x+NaNi (for any finite x), the result is NaN+NaNi and FE_INVALID may be raised
• If z is -∞+yi (for any finite positive y), the result is +∞+πi
• If z is +∞+yi (for any finite positive y), the result is +∞+0i
• If z is -∞+∞i, the result is +∞+3πi/4
• If z is +∞+∞i, the result is +∞+πi/4
• If z is ±∞+NaNi, the result is +∞+NaNi
• If z is NaN+yi (for any finite y), the result is NaN+NaNi and FE_INVALID may be raised
• If z is NaN+∞i, the result is +∞+NaNi
• If z is NaN+NaNi, the result is NaN+NaNi

### Notes

The natural logarithm of a complex number z with polar coordinate components (r,θ) equals ln r + i(θ+2nπ), with the principal value ln r + iθ

### Example

#include <stdio.h>
#include <math.h>
#include <complex.h>

int main(void)
{
double complex z = clog(I); // r = 1, θ = pi/2
printf("2*log(i) = %.1f%+fi\n", creal(2*z), cimag(2*z));

double complex z2 = clog(sqrt(2)/2 + sqrt(2)/2*I); // r = 1, θ = pi/4
printf("4*log(sqrt(2)/2+sqrt(2)i/2) = %.1f%+fi\n", creal(4*z2), cimag(4*z2));

double complex z3 = clog(-1); // r = 1, θ = pi
printf("log(-1+0i) = %.1f%+fi\n", creal(z3), cimag(z3));

double complex z4 = clog(conj(-1)); // or clog(CMPLX(-1, -0.0)) in C11
printf("log(-1-0i) (the other side of the cut) = %.1f%+fi\n", creal(z4), cimag(z4));
}

Output:

2*log(i) = 0.0+3.141593i
4*log(sqrt(2)/2+sqrt(2)i/2) = 0.0+3.141593i
log(-1+0i) = 0.0+3.141593i
log(-1-0i) (the other side of the cut) = 0.0-3.141593i

### References

• C11 standard (ISO/IEC 9899:2011):
• 7.3.7.2 The clog functions (p: 195)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• G.6.3.2 The clog functions (p: 543-544)
• G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
• 7.3.7.2 The clog functions (p: 176-177)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• G.6.3.2 The clog functions (p: 478-479)
• G.7 Type-generic math <tgmath.h> (p: 480)